Advances in high-Q piezoelectric resonator materials and devices

In order to compare piezoelectric materials and devices, an intrinsic parameter, the motional time constant tau(1)/sup (m/)=(omega/sub m/Q/sub m/)(-1) for a particular mode m is employed. The use of tau(1)/sup (m/) follows from the accommodation of acoustic loss in the elastic compliance/stiffness and the establishment of material coefficients that are elements of viscosity matrices. Alternative and fully equivalent definitions of tau(1) are given based on the RC time constant derived from the equivalent circuit representation of a crystal resonator, acoustic attenuation, logarithmic decrement, and viscosity or damping. For quartz devices, the variation of tau(1): for any simple thickness mode, for the Y'X shear mode for rotated Y-cuts, and with diameter-thickness ratio for AT-cuts is discussed. Other factors such as mounting loss and loss caused by crystal inhomogeneities (dislocations, defect positions in the resonator, and impurity migration under vibrational stress) are briefly considered with quartz devices as the model. Some new piezoelectric materials/material constants/devices are reviewed and their motional time constants are compared. A physical parameter, composed of acoustic velocity, piezoelectric coupling, and tau(1) is identified which aids in understanding the maximum frequency limitations of plate resonators.